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%I #12 Feb 14 2015 21:07:35
%S 3,5,7,13,17,29,97,113,193,257,449,509,769,7937,12289,65537,114689,
%T 520193,786433,7340033,8388593,33292289,33550337,469762049,2130706433,
%U 3221225473,8588886017,137438691329,206158430209
%N Cototient(totient(n))=A070556(n) is a power of 2 and n is a prime number.
%e Powers of 2 observable in A070556[this sequence] = {1, 2, 4, 8, 16, 64, 128, 256, 512, 4096, 8192, 32768, 65536, 262144, 524288, ...}. For F(m), Fermat prime:phi[F(m)]=2^m, cototient[2^m]=2^(m-1); if n=113: phi[113]=112, cototient[112]=112-48=64, so 113 is in this sequence.
%t Do[s= EulerPhi[n]-EulerPhi[EulerPhi[n]]; If[IntegerQ[Log[2, s]]&&PrimeQ[n], Print[n]], {n, 1, 10000000}]
%o (PARI) ispow2(n)=n==1<<valuation(n,2);
%o forprime(p=2,4e9,if(ispow2(p-1-eulerphi(p-1)),print1(p", "))) \\ _Charles R Greathouse IV_, May 17 2011
%Y Cf. A070556, A051953, A054571, A070807, A070809-A070811.
%K nonn
%O 1,1
%A _Labos Elemer_, May 08 2002
%E a(20)-a(27) from _Donovan Johnson_, Feb 06 2010
%E a(28)-a(29) from _Charles R Greathouse IV_, May 17 2011
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